Conventional digital signal processing techniques consider signals that are represented by a set a uniformly spaced sampled values. Although most processing algorithms are derived within a purely discrete framework, there are a variety of biomedical problems (e.g., detection of anatomical structures in images, estimation of velocity from sequences of x-y coordinates) that would be better formulated by considering a signal as a continuous real-valued function defined over some domain. This study is concerned with the development of new processing techniques that represent signals by continuous polynomial spline functions. Traditionally, polynomial spline interpolation or approximation problems are approached using a matrix formulation. Our initial contribution has been to derive efficient computational algorithms using recursive digital filters. These techniques have been applied to the design of fast algorithms for image interpolation and compression. more recently, we have derived a sampling theory for polynomial splines that generalizes Shannon's sampling theorem for bandlimited functions. We have also defined a whole family of polynomial spline wavelet transforms that allows the expansion of continuous image functions in terms of basis functions that are obtained by dilatation and expansion of a single prototype. Such wavelet transforms may provide space/frequency signal decompositions that are close-to-optimal according to the uncertainty principle.